Question

You wish to test the following claim (Ha) at a significance level of α=0.001.

      Ho:μ=57.4
      Ha:μ>57.4

You believe the population is normally distributed and you know the standard deviation is σ=6.6. You obtain a sample mean of M=59.7 for a sample of size n=72.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

in the critical region

not in the critical region

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 57.4.

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 57.4.

The sample data support the claim that the population mean is greater than 57.4.

There is not sufficient sample evidence to support the claim that the population mean is greater than 57.4.

Answer 1

Solution:

    Given:

We have to test the following claim (Ha) at a significance level of α=0.001.

      H_o: μ = 57.4
      H_a: μ > 57.4

The population is normally distributed

Population standard deviation = σ = 6.6.

Sample mean = M=59.7

Sample size = n = 72.

Part a) What is the critical value for this test?

significance level of α=0.001

Since this is right tailed test, look in z table for

Area = 1 - 0.001 = 0.9990 or its closest area and find z value.

Area 0.9990 corresponds to 3.0 and 0.09

thuz z critical value = 3.09

z critical = 3.090

Part b) What is the test statistic for this sample?

Part c) The test statistic is...?

The test statistic is = 2.957 < z critical value = 3.090, hence the test statistic is not in the critical region.

Part d) This test statistic leads to a decision to fail to reject the null.

Part e) As such, the final conclusion is that:

There is not sufficient sample evidence to support the claim that the population mean is greater than 57.4.